Finite Group Databasebeta

← #15760518

Subgroups — #15760518

Order 3328.

504 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125296C211yesmaximal, characteristic
2#13113571C211yesmaximal, characteristic
3#13113520C212yesmaximal, complemented
4#13112727C212yesmaximal, complemented
5C13×#2979C211yesmaximal, characteristic
6C13×#532C2211yescharacteristic
7C2×#88205—22no—
8C2×#88123C2211yescharacteristic
9C13×#436—22no—
10C8×D4×C13—22no—
11C13×#431C2212yes—
12C13×#408—22no—
13#11718753—21no—
14#11718737—21no—
15#11718721C414yes—
16#11718585C2212yes—
17C4×#6099C2211yescharacteristic
18#11718138—21no—
19#11718136—21no—
20#11718074—22no—
21#11718074—22no—
22C2×C13×#41D412yes—
23C22×Dic26—21no—
24C2×C13×M16—22no—
25C22×C8×C13—22no—
26C13×C4⋊Q8D411yescharacteristic
27C13×#127D411yescharacteristic
28C13×#124C2×C412yes—
29C13×#121—22no—
30C4×D4×C13—22no—
31C2×C42×C13C2311yescharacteristic
32#88205—44no—
33#88205—44no—
34C2×#6107—24no—
35C2×#6105—24no—
36C2×C4⋊Dic13—22no—
37C2×#6099—21no—
38C2×#6099—22no—
39#88123—22no—
40#88123—21no—
41#88123C2×C412yes—
42C13×C4⋊C8D412yes—
43C13×C4⋊C8D412yes—
44C13×C22⋊C8—24no—
45C13×C22⋊C8—22no—
46C4×C8×C13—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49#88043C2×C412yes—
50C4×#1055—21no—
51#9435—131nomaximal, Sylow
52C13×#41—42no—
53C13×#41—42no—
54C2×Q8×C13C22⋊C412yes—
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13C22⋊C412yes—
58C22×C4×C13—22no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13#4112yes—
61C22×Dic13—41no—
62C2×Dic26—22no—
63C2×Dic26—42no—
64C2×Dic26—42no—
65C2×Dic26—41no—
66C13×M16—82no—
67C2×C8×C13—22no—
68C2×C8×C13—22no—
69C2×C8×C13—82no—
70C13×C4⋊C4—22no—
71C13×C22⋊C4—24no—
72C42×C13C22×C411yescharacteristic
73C42×C13C2×D411yescharacteristic
74C42×C13C2×D412yes—
75#6107—48no—
76#6105—48no—
77C4⋊Dic13—24no—
78C4⋊Dic13—42no—
79#6099—22no—
80#6099—22no—
81#6099—82no—
82C2×#1055—22no—
83C2×#1055—42no—
84#3152—131no—
85#2979D1311yescharacteristic
86#1560—131no—
87#1549—132no—
88#1299—132no—
89C23×C13—22no—
90C23×C13#12311yescharacteristic
91Q8×C13—42no—
92D4×C13—42no—
93D4×C13—42no—
94D4×C13—42no—
95D4×C13—82no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13C4×D412yes—
105C2×C4×C13#12011yescharacteristic
106C2×C4×C13#12112yes—
107C2×Dic13—42no—
108C2×Dic13—82no—
109Dic26—44no—
110Dic26—81no—
111Dic26—81no—
112C8×C13—42no—
113C8×C13—42no—
114#1055—24no—
115#1055—82no—
116C2×#137—262no—
117#532C2×D1311yescharacteristic
118C2×C4⋊Q8—131no—
119#497—134no—
120#494—261no—
121#492—261no—
122#436—22no—
123C8×D4—22no—
124#431C2×D1312yes—
125#423—132no—
126#408—22no—
127C4×M16—131no—
128#333—261no—
129#332—262no—
130#332—262no—
131#331—261no—
132C22×C13—21no—
133C22×C13—22no—
134C22×C13—42no—
135C22×C13—44no—
136C22×C13#38611yescharacteristic
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—42no—
140C4×C13#45311yescharacteristic
141C4×C13#45311yescharacteristic
142C4×C13#47112yes—
143C4×C13#47312yes—
144Dic13—82no—
145C2×#41C22⋊D1312yes—
146C22×Q8—261no—
147#137—524no—
148#137—524no—
149C2×Q16—264no—
150C2×SD16—264no—
151C2×M16—22no—
152C2×M16—261no—
153C2×M16—262no—
154C22×C8—22no—
155C4⋊Q8—132no—
156C4⋊Q8—261no—
157C4⋊Q8—262no—
158C4⋊Q8D5211yescharacteristic
159#127D5211yescharacteristic
160#124C4×D1312yes—
161#121—22no—
162C4×D4—22no—
163C2×C4⋊C4—262no—
164C2×C42C22×D1311yescharacteristic
165C4⋊C8—262no—
166C4⋊C8—262no—
167C4⋊C8C22⋊D1312yes—
168C4⋊C8C22⋊D1312yes—
169C22⋊C8—24no—
170C22⋊C8—22no—
171#97—132no—
172C4×C8—22no—
173C4×C8—261no—
174C2×C13—41no—
175C2×C13—82no—
176C2×C13#188711yescharacteristic
177C2×C13#190812yes—
178#41—42no—
179#41—42no—
180C2×Q8—262no—
181C2×Q8—522no—
182C2×Q8—522no—
183C2×Q8—521no—
184C2×Q8#610312yes—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4#610312yes—
188C22×C4—22no—
189C22×C4—521no—
190C22×C4#612712yes—
191C22×C4C2×C22⋊D1311yescharacteristic
192Q16—528no—
193SD16—528no—
194M16—82no—
195M16—262no—
196M16—262no—
197M16—1042no—
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—82no—
201C2×C8—262no—
202C2×C8—522no—
203C4⋊C4—22no—
204C4⋊C4—264no—
205C4⋊C4—522no—
206C22⋊C4—24no—
207C42C2×C4×D1311yescharacteristic
208C42C2×D5211yescharacteristic
209C42C2×C22⋊D1312yes—
210C13#943511yescharacteristic, complemented, Sylow
211C23—22no—
212C23#8818311yescharacteristic
213Q8—42no—
214Q8—524no—
215Q8—1041no—
216Q8—1041no—
217D4—42no—
218D4—42no—
219D4—42no—
220D4—82no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—522no—
229C2×C4—1042no—
230C2×C4C2×#610311yescharacteristic
231C2×C4C4×C22⋊D1312yes—
232C2×C4#8818412yes—
233C2×C4#8820711yescharacteristic
234C8—42no—
235C8—42no—
236C8—264no—
237C8—1042no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—44no—
242C22#1171887411yescharacteristic
243C4—21no—
244C4—22no—
245C4—42no—
246C4—1042no—
247C4#1171880212yes—
248C4#1171880412yes—
249C4#1171890211yescharacteristic
250C4#1171890211yescharacteristic
251C2—41no—
252C2—82no—
253C2#1311523411yescharacteristic
254C2#1311535112yes—
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2979C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#2979D13
hypocenterC13#9435
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2979

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13113520C2semidirect
4. #13112727C2semidirect
210. C13#9435semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131252962
#131135712
#131135202
#131127272
C13×#29792
#943513